scholarly journals Gromov minimal fillings for finite metric spaces

2013 ◽  
Vol 94 (108) ◽  
pp. 3-15
Author(s):  
Alexander Ivanov ◽  
Alexey Tuzhilin
Keyword(s):  
Metric Spaces ◽  
State University ◽  
Steiner Ratio ◽  
Chip Design ◽  
New Approach ◽  
One Dimensional ◽  
Design Evolution ◽  
Steiner Minimal Trees ◽  
Finite Metric Spaces ◽  
Moscow State University

The problem discussed in this paper was stated by Alexander O. Ivanov and Alexey A. Tuzhilin in 2009. It stands at the intersection of the theories of Gromov minimal fillings and Steiner minimal trees. Thus, it can be considered as one-dimensional stratified version of the Gromov minimal fillings problem. Here we state the problem; discuss various properties of one-dimensional minimal fillings, including a formula calculating their weights in terms of some special metrics characteristics of the metric spaces they join (it was obtained by A.Yu. Eremin after many fruitful discussions with participants of Ivanov-Tuzhilin seminar at Moscow State University); show various examples illustrating how one can apply the developed theory to get nontrivial results; discuss the connection with additive spaces appearing in bioinformatics and classical Steiner minimal trees having many applications, say, in transportation problem, chip design, evolution theory etc. In particular, we generalize the concept of Steiner ratio and get a few of its modifications defined by means of minimal fillings, which could give a new approach to attack the long standing Gilbert-Pollack Conjecture on the Steiner ratio of the Euclidean plane.

scholarly journals Target optimization of a supercomputer task flow

2019 ◽  
pp. 199-210
Author(s):  
С.Н. Леоненков
Keyword(s):  
Performance Characteristics ◽  
State University ◽  
Efficiency Function ◽  
New Approach ◽  
Basic Performance ◽  
University Experience ◽  
Supercomputer Systems ◽  
Moscow State University

Настоящая статья является результатом исследования потока задач суперкомпьютеров "Ломоносов" и "Ломоносов-2". Предложен подход к оценке эффективности функционирования суперкомпьютерной системы, основанный на ее базовых характеристиках. Введена новая функция потери качества планирования суперкомпьютера. Подход позволяет сравнивать разные суперкомпьютерные системы исходя из целей использования, которые стоят перед системными администраторами вычислительных центров. Описан опыт применения целевой оптимизации процессов планирования, основанной на предложенном подходе, для суперкомпьютеров "Ломоносов" и "Ломоносов-2". This paper is a result of studying the task flows observed on the Lomonosov and Lomonosov-2 supercomputers. A new approach to evaluating the performance of a supercomputer system based on its basic performance characteristics is proposed. A supercomputer's scheduling efficiency function is introduced for Lomonosov, Lomonosov-2 and other systems. The approach allows the system administrators to compare various supercomputer systems based on their usage aims. This paper describes the Moscow State University experience of applying the proposed approach to the optimization of Lomonosov and Lomonosov-2 scheduling resources.

scholarly journals A New Approach to Teaching C++ Programming for Cartography Students by Means Training Programs with Emphasizing Cartography and Geodesy

2019 ◽  
Vol 2 ◽  
pp. 1-6
Author(s):  
Vladimir Zablotskii
Keyword(s):  
Training Programs ◽  
Object Oriented Programming ◽  
State University ◽  
Topographic Map ◽  
New Approach ◽  
C Programming ◽  
Angular Measurements ◽  
Approach To Teaching ◽  
Training Modules ◽  
Moscow State University

<p><strong>Abstract.</strong> A new course of C++ programming for cartographers and surveyors has been developed. Pedagogical experiments were carried out in the period of 2009–2019 in Moscow State University of Geodesy and Cartography. The new course focuses on the use of cartographic tasks and geodetic exercises to illustrate various programming language constructions. Direct and inverse geodetic problem, position determination via a topographic map, work with a theodolite when performing angular measurements, leveling, etc. are considered in training modules. Programs are used as supporting data during the lectures, and as tasks for practical. This is the main purpose of the training. Currently, more than fifty training programs are used in the training process. All programs contain no more than 60 lines of code to ease the understanding of the program by students. The examples the typical training programs for students studying the C++ are discussed. The first program Theodolite is designed to study the concept of class, constructor, destructor, and object-oriented programming in general. The second program focuses to solve the inverse of the geodetic task.</p>

scholarly journals Metrics transformations preserving the types of one-dimensional minimal fillings

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1081-1089
Author(s):  
S.Yu. Lipatova
Keyword(s):  
Metric Spaces ◽  
Diagonal Matrix ◽  
Ultrametric Spaces ◽  
One Dimensional ◽  
Positive Elements ◽  
The Matrix ◽  
Finite Metric Spaces ◽  
Class F

Given a class F of metric spaces and a family of transformations T of a metric, one has to describe a family of transformations T' ? T that transfer F into itself and preserve some types of minimal fillings. The article considers four cases. First, when F is the class of all finite metric spaces, T = {(M,?) ? (M, f??) | f : R>0 ? R>0}, and the elements of T' preserve all non-degenerate types of minimal fillings of four-point metric spaces and finite non-degenerate stars, and we prove that T' = {(M,?) ? (M,?? + a):a > ?a?}. Second, when F is the class of all finite metric spaces, the class T consists of the maps ? ? N?, where the matrix N is the sum of a positive diagonal matrix A and a matrix with the same rows of non-negative elements. The elements of T' preserve all minimal fillings of the type of non-degenerate stars. It has been proven that T0 consists of maps ? ? N? where A is scalar. Third, when F is the class of all finite additive metric spaces, T is the class of all linear mappings given by matrices, and the elements of T' preserve all non-degenerate types of minimal fillings, and we proved that for metric spaces consisting of at least four points T' is the set of transformations given by scalar matrices. Fourth, when F is the class of all finite ultrametric spaces, T is the class of all linear mappings given by matrices, and we proved that for threepoint spaces the matrices have the form A = R(B + ?E), where B is a matrix of identical rows of positive elements, and R is a permutation of the points (1,0,0),(0,1,0) and (0,0,1).

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